1. Field of the Invention
The present invention is directed to a method for image reconstruction in a computed tomography apparatus of the type wherein measured values S(.beta., .alpha.) are obtained by a radiation source in fan geometry that is movable around a system axis around a measuring field in which an examination subject is disposed, wherein .alpha. is the projection angle and .beta. is the fan angle of the measured values, and wherein only the minimally possible projection angle range .alpha..sub.g (.beta.) for the respective fan angle .beta. is employed for all measured values S(.beta., .alpha.) of the same fan angle .beta., with the minimally possible projection angle range .alpha..sub.g (.beta.) being established by the equation .alpha..sub.g (.beta.)=.PI.-2.beta..
2. Description of the Prior Art
When imaging time-variable processes, a high time resolution of the presentation is of great significance. In the field of computed tomography, time-variable events are, for example, movements of the heart muscle or of the heart valves, movements in the mediastinum induced by the heart activity or peristaltic movements. Known methods for improving time resolution in computed tomography exposures are sub-revolution exposures with a computed tomography system of the third or fourth generations, or exposures with an electron beam tomography (EBT) apparatus.
The measuring time interval t.sub.Q from which measured values take effect in an image serves as rough measure for the time resolution realized in an image. More precise statements with respect to the time resolution are possible on the basis of time sensitivity profiles.
A reduction of the measuring time interval t.sub.Q can ensue either by reducing the angular range to be swept when scanning an examination subject given a constant angular velocity, or by increasing the angular velocity of the scan given a constant angular range. The first possibility is used in sub-revolution exposures, namely for also shortening the measuring time interval t.sub.Q by registering measured values over less then 360.degree..
When the measured values S(.beta., .alpha.) according to FIG. 1 (which can also be employed to practice the invention) are registered in fan geometry (.beta. is the fan angle; .alpha. is the projection angle), then the condition for a minimal projection angle range is formulated as follows. Given a full revolution (simple revolution) of 2.PI., there is a complementary measured value S(.beta.;.alpha.), for each measured value S(.beta.,.alpha.) characterized by .alpha. and .beta., this having been registered from the opposite direction. This complementary measured value is redundant. It is therefore obviously allowable to select that projection angle range as minimal projection angle range for each .beta. that happens to contain no complementary measured values at the moment. The attenuation value S(.beta.;.alpha.)complementary to S(.beta.,.alpha.) is the attenuation value given the angles EQU .alpha.=.alpha.+2.beta..+-..PI., .beta.=-.beta.. (1)
Enough measured values must then be available for each fan angle .beta. so that the remainder up to 2.PI. contains only complementary values. For the minimal revolution angle .alpha..sub.g (.beta.), i.e. the minimal projection angle range, EQU .alpha..sub.g (.beta.)=.PI.-2.beta. (2)
applies.
The equality .alpha..sub.g (.beta.=0)=.PI. arises for the central channel of the detector (.alpha.=0). However, .alpha..sub.g (-.beta..sub.fan /2)=.PI.+.beta..sub.fan is required for the channel .beta.=-.beta..sub.fan /2 (.beta..sub.fan is the overall fan angle of the detector), i.e. a larger projection angle range than .PI.. The channel .beta.=.beta..sub.fan /2 of the projection angle range .alpha..sub.g (-.beta..sub.fan /2)=.PI.-.beta..sub.fan is adequate for this purpose.
The maximally required projection angle range .alpha..sub.g (-.beta..sub.fan /2)=.PI.+.beta..sub.fan has been employed for all fan angles .beta. in conventional sub-revolution reconstructions. This projection angle range, however, is only really required for the channel .beta.=-.beta..sub.fan /2; by contrast thereto, there are direct as well as complementary measured values in a part of the projection angle range for all other fan angles that are suitably averaged for reasons of dose utilization.
In order to reduce line artifacts, a discontinuous transition between direct and complementary measured values is often avoided by a soft transition weighting having the width .alpha..sub.tans. The necessary projection angle range is enlarged by .alpha..sub.trans as a result. Conventionally, thus, the projection angle range EQU .alpha..sub.Q =.PI.+.beta..sub.fan +.alpha..sub.trans (3)
is employed for all fan angles .beta. for sub-revolution reconstruction and not only for .beta.=-.beta..sub.fan /2. This is obvious since this projection angle range is in fact registered in the measurement for all fan angles. The conventional sub-revolution reconstruction therefore is optimized with respect to the dose utilization of a sub-revolution exposure, but is not optimized with respect to the best possible time resolution, as is required given exposures of moving subjects (for example, a beating heart).
In conventional sub-revolution reconstruction, the measuring time interval ##EQU1##
contributes to the image for each picture element. The time t.sub.rot is the time for a full revolution of the scanner. For example, t.sub.Q amounts to t.sub.Q =0.5s=0.66 t.sub.rot for all picture elements with t.sub.rot =0.75s, .beta..sub.fan =52.degree. and .alpha..sub.trans =8.degree..
Conventional sub-revolution exposures in fan geometry thus have two disadvantages with respect to the time resolution. First, an exposure time of only half a second is achieved even given the fastest computed tomography systems of the third or fourth generations currently available, which still is not sufficient given higher pulse rates in order, for example, to be able to calculate a cardiac exposure during the relaxation phase. Second, the sequential registration of successive sub-revolution exposures prevents a rapid time scanning of the event of interest.
When the measured values S(p, .crclbar.) (p is the spacing of the line integral from the rotational center of the computed tomography system (.crclbar. is the projection angle) are already registered in parallel geometry, then it is sufficient to cover only a projection angle range of .PI.. Accordingly, an image-effective exposure time (measuring time interval) of t.sub.Q =0.5 t.sub.rot can be achieved. No apparatus is currently known, however, that can register true parallel data in one second or less. This possibility is thus eliminated for practical use.
The concept underlying electron beam tomography is to increase the angular velocity of the scan by suppressing mechanical components in order to reduce the measuring time interval t.sub.Q. Systems have been produced that require only 50 ms for an individual scan of the patient. These systems, however, have two disadvantages. First, their costs are considerably higher than those of conventional computed tomography systems. Second, a number of scans of the subject are usually required for calculating images that do not have an excessively high noise level, as a result of which the gain in the reduction of the exposure time is reduced.
A method of the type initially described is disclosed in European Application 0 426 464. This method offers the advantage of a short calculating time since no more measured values than are absolutely required are employed.